Whakaoti i te 2/3-x+1/2=6/x(3-x)

$$\frac { 2 } { 3 - x } + \frac { 1 } { 2 } = \frac { 6 } { x ( 3 - x ) }$$

Whakaoti mō x

$$x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3-x,2,x\left(3-x\right).

$$-2x\times 2+2x\left(x-3\right)\times \frac{1}{2}=-2\times 6$$

Whakareatia te -2 ki te 2, ka -4.

$$-4x+2x\left(x-3\right)\times \frac{1}{2}=-2\times 6$$

Whakareatia te 2 ki te \frac{1}{2}, ka 1.

$$-4x+x\left(x-3\right)=-2\times 6$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$-4x+x^{2}-3x=-2\times 6$$

Pahekotia te -4x me -3x, ka -7x.

$$-7x+x^{2}=-2\times 6$$

Whakareatia te -2 ki te 6, ka -12.

$$-7x+x^{2}=-12$$

Me tāpiri te 12 ki ngā taha e rua.

$$-7x+x^{2}+12=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-7x+12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -7 mō b, me 12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 12}}{2}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 12}}{2}$$

Whakareatia -4 ki te 12.

$$x=\frac{-\left(-7\right)±\sqrt{49-48}}{2}$$

Tāpiri 49 ki te -48.

$$x=\frac{-\left(-7\right)±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-\left(-7\right)±1}{2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±1}{2}$$

Nā, me whakaoti te whārite x=\frac{7±1}{2} ina he tāpiri te ±. Tāpiri 7 ki te 1.

$$x=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{7±1}{2} ina he tango te ±. Tango 1 mai i 7.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Kua oti te whārite te whakatau.

$$x=4 x=3$$

Tē taea kia ōrite te tāupe x ki 3.

$$x=4$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 0,3 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x\left(x-3\right), arā, te tauraro pātahi he tino iti rawa te kitea o 3-x,2,x\left(3-x\right).

$$-2x\times 2+2x\left(x-3\right)\times \frac{1}{2}=-2\times 6$$

Whakareatia te -2 ki te 2, ka -4.

$$-4x+2x\left(x-3\right)\times \frac{1}{2}=-2\times 6$$

Whakareatia te 2 ki te \frac{1}{2}, ka 1.

$$-4x+x\left(x-3\right)=-2\times 6$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$-4x+x^{2}-3x=-2\times 6$$

Pahekotia te -4x me -3x, ka -7x.

$$-7x+x^{2}=-2\times 6$$

Whakareatia te -2 ki te 6, ka -12.

$$-7x+x^{2}=-12$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}-7x=-12$$

Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-12+\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-7x+\frac{49}{4}=-12+\frac{49}{4}$$

Tāpiri -12 ki te \frac{49}{4}.

$$x^{2}-7x+\frac{49}{4}=\frac{1}{4}$$

Tauwehea x^{2}-7x+\frac{49}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{1}{4}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{1}{2} x-\frac{7}{2}=-\frac{1}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=4 x=3$$

Tē taea kia ōrite te tāupe x ki 3.

$$x=4$$